Problem: Rewrite as a simplified fraction. ${0.61\overline{6} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 616.6666...\\ 100x &= 61.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 555}$ ${x = \dfrac{555}{900}} $ ${x = \dfrac{37}{60}} $